Sofie Coene

On a periodic vehicle routing problem

This paper deals with a study on a variant of the Periodic Vehicle Routing Problem (PVRP). As in the traditional Vehicle Routing Problem, customer locations each with a certain daily demand are given, as well as a set of capacitated vehicles. In addition, the PVRP has a horizon, say T days, and there is a frequency for each customer stating how often within this T-day period this customer must be visited. A solution to the PVRP consists of T sets of routes that jointly satisfy the demand constraints and the frequency constraints. The objective is to minimize the sum of the costs of all routes over the planning horizon. We develop different algorithms solving the instances of the case studied. Using these algorithms we are able to realize considerable cost reductions compared to the current situation.

The accessibility arc upgrading problem

The accessibility arc upgrading problem (AAUP) is a network upgrading problem that arises in real-life decision processes such as rural network planning. In this paper, we propose a linear integer programming formulation and two solution approaches for this problem. The first approach is based on the knapsack problem and uses the knowledge gathered from an analytical study of some special cases of the AAUP. The second approach is a variable neighbourhood search with strategic oscillation. The excellent performance of both approaches is demonstrated using a large set of randomly generated instances. Finally, we stress the importance of a proper allocation of scarce resources in accessibility improvement.

The Lockmaster's Problem

Inland waterways form a natural network infrastructure with capacity for more traffic. Transportation by ship is widely promoted as it is a reliable, efficient and environmental friendly way of transport. Nevertheless, locks managing the water level on waterways and within harbors sometimes constitute bottlenecks for transportation over water. The lockmaster’s problem concerns the optimal strategy for operating such a lock. In the lockmaster’s problem we are given a lock, a set of upstream-bound ships and another set of ships traveling in the opposite direction. We are given the arrival times of the ships and a constant lockage time; the goal is to minimize total waiting time of the ships. In this paper, a dynamic programming algorithm is proposed that solves the lockmaster’s problem in polynomial time. This algorithm can also be used to solve a single batching machine scheduling problem more efficiently than the current algorithms from the literature do. We extend the algorithm such that it can be applied in realistic settings, taking into account capacity, ship-dependent handling times, weights and water usage. In addition, we compare the performance of this new exact algorithm with the performance of some (straightforward) heuristics in a computational study.

Balancing Profits and Costs on Trees

We consider a rooted tree graph with costs associated with the edges and profits associated with the vertices. Every subtree containing the root incurs the sum of the costs of its edges, and collects the sum of the profits of its nodes; the goal is the simultaneous minimization of the total cost and maximization of the total profit. This problem is related to the TSP with profits on graphs with a tree metric. We analyze the problem from a biobjective point of view. We show that finding all extreme supported efficient points can be done in polynomial time. The problem of finding all efficient points, however, is harder; we propose a practical FPTAS for solving this problem. Some special cases are considered where the particular profit/cost structure or graph topology allows the efficient points to be found in polynomial time. Our results can be extended to more general graphs with distance matrices satisfying the Kalmanson conditions.

The Lockmaster's problem

Inland waterways form a natural network that is an existing, congestion free infrastructure with capacity for more traffic. The European commission promotes the transportation of goods by ship as it is a reliable, efficient and environmental friendly way of transport. A bottleneck for transportation over water are the locks that manage the water level. The lockmasters problem concerns the optimal strategy for operating such a lock. In the lockmasters problem we are given a lock, a set of ships coming from downstream that want to go upstream, and another set of ships coming from upstream that want to go downstream. We are given the arrival times of the ships and a constant lockage time; the goal is to minimize total waiting time of the ships. In this paper a dynamic programming algorithm (DP) is proposed that solves the lockmasters problem in polynomial time. We extend this DP to different generalizations that consider weights, water usage, capacity, and (a fixed number of) multiple chambers. Finally, we prove that the problem becomes strongly NP-hard when the number of chambers is part of the input.

Charlemagne's Challenge: The Periodic Latency Problem

Latency problems are characterized by their focus on minimizing total waiting time for all clients. We consider periodic latency problems: an extension of standard latency problems. In a periodic latency problem each client has to be visited regularly. More precisely, given is a server traveling at unit speed, and a set of clients with their positions. To each client a periodicity is associated that is the maximal amount of time that is allowed to pass between consecutive visits of the server to that client. In a problem we denote as PLPP, the goal is then to find a repeatable route for the server visiting as many clients as possible without violating the periodicities. Further, we consider the PLP in which the number of servers needed to serve all clients is minimized. We give polynomial-time algorithms and NP-hardness results for these problems depending upon the topology of the underlying network.

The Periodic Vehicle Routing Problem: A Case Study

This paper deals with a case study which is a variant of the Periodic Vehicle Routing Problem (PVRP). As in the traditional Vehicle Routing Problem (VRP), customer locations each with a certain daily demand are given, as well as a set of capacitated vehicles. In addition, the PVRP has a horizon, say T days, and there is a frequency for each customer stating how often within this T-day period this customer must be visited.A solution to the PVRP consists of T sets of routes that jointly satisfy the demand constraints and the frequency constraints. The objective is to minimize the sum of the costs of all routes over the planning horizon. We develop different algorithms solving the instances of the case studied. Using these algorithms we are able to realize considerable cost reductions compared to the current situation.

On the Computational Complexity of Peer-to-Peer Satellite Refueling Strategies

Abstract We revisit the peer-to-peer on-orbit satellite refueling problem, in which the maneuvering satellites are allowed to interchange their orbital positions. We show that the problem is computationally hard by reducing it to a special case of the three-index assignment problem. On the positive side, we show that the size of instances in practice is such that a state-of-the-art integer programming solver is able to find globally optimal solutions in little computing time.

Heuristics for the traveling repairman problem with profits

In the traveling repairman problem with profits, a repairman (also known as the server) visits a subset of nodes in order to collect time-dependent profits. The objective consists of maximizing the total collected revenue. We restrict our study to the case of a single server with nodes located in the Euclidean plane. We investigate properties of this problem, and we derive a mathematical model assuming that the number of visited nodes is known in advance. We describe a tabu search algorithm with multiple neighborhoods, and we test its performance by running it on instances based on TSPLIB. We conclude that the tabu search algorithm finds good-quality solutions fast, even for large instances.

A Note on Peer-to-Peer Satellite Refueling Strategies

We revisit the peer-to-peer refueling problem, in which the maneuvering satellites are allowed to interchange their orbital positions [2]. We show that the problem is computationally hard, by reducing it to a special case of the three-index assignment problem. On the positive side, we show that the size of instances from practice is such that a state-of-the-art integer programming solver is able to find optimal solutions in little computing time.